Problem: Nastya likes reading and even spends whole days in a library sometimes. Today she found a chronicle of Byteland in the library, and it stated that there lived shamans long time ago. It is known that at every moment there was exactly one shaman in Byteland, and there were n shamans in total enumerated with integers from 1 to n in the order they lived. Also, each shaman had a magic power which can now be expressed as an integer.

The chronicle includes a list of powers of the n shamans. Also, some shamans can be king-shamans, if they gathered all the power of their predecessors, i.e. their power is exactly the sum of powers of all previous shamans. Nastya is interested in whether there was at least one king-shaman in Byteland.

Unfortunately many of the powers are unreadable in the list, so Nastya is doing the following:

  * Initially she supposes some power for each shaman. 
  * After that she changes the power of some shaman q times (the shamans can differ) and after that wants to check if there is at least one king-shaman in the list. If yes, she wants to know the index of any king-shaman. 



Unfortunately the list is too large and Nastya wants you to help her.

Input

The first line contains two integers n and q (1 ≤ n, q ≤ 2·105).

The second line contains n integers a1, ..., an (0 ≤ ai ≤ 109), where ai is the magic power of the i-th shaman.

After that q lines follow, the i-th of them contains two integers pi and xi (1 ≤ pi ≤ n, 0 ≤ xi ≤ 109) that mean that the new power of the pi-th shaman is xi.

Output

Print q lines, the i-th of them should contain  - 1, if after the i-th change there are no shaman-kings, and otherwise a single integer j, where j is an index of some king-shaman after the i-th change.

If there are multiple king-shamans after each change, print the index of any of them.

Examples

Input

2 1
1 3
1 2


Output

-1


Input

3 4
2 2 3
1 1
1 2
2 4
3 6


Output

3
2
-1
3


Input

10 7
0 3 1 4 6 2 7 8 10 1
2 5
1 3
9 36
4 10
4 9
1 2
1 0


Output

1
-1
9
-1
4
-1
1

Note

In the first example powers of shamans after the first change are equal to (2, 3). The answer equals  - 1, because the sum of powers of shamans before the first shaman is equal to 0, and before the second is equal to 2.

In the second example after the first change the powers are equal to (1, 2, 3). The answer is equal to 3, because the power of the third shaman is equal to 3, and the sum of powers of the first and the second shaman is also 1 + 2 = 3. After the second change the powers become equal to (2, 2, 3), where the answer equals 2. After the third change the powers become equal to (2, 4, 3), where the answer equals  - 1. After the fourth change the powers become equal to (2, 4, 6), where the answer equals 3.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.StringTokenizer;


public class Main {

    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        int n = sc.nextInt();
        int q = sc.nextInt();
        int[] a = sc.nextIntArray(n);
        SegmentTree st = new SegmentTree(a);
        loop:
        while (q-- > 0) {
            int p = sc.nextInt();
            int x = sc.nextInt();
            st.pointUpdate(p, x);
            if (st.sTree[1] == 0) {
                out.println(1);
                continue;
            }
            long s = 2 * st.sTree[st.N];
            while (true) {
                int idx = st.query(s);
                if (idx == -1) break;
                long before = st.getCum(idx);
                long val = st.sTree[st.N - 1 + idx];
                if (val == before) {
                    out.println(idx);
                    continue loop;
                }
                s = (val + before) * 2;
            }
            out.println(-1);
        }
        out.flush();
        out.close();
    }

    static public class SegmentTree {
        int N;
        int[] array;
        long[] sTree;

        public SegmentTree(int[] in) {
            N = 1;
            while (N < in.length)
                N <<= 1;
            array = new int[N + 1];
            for (int i = 0; i < in.length; i++)
                array[i + 1] = in[i];
            sTree = new long[N << 1];
            build(1, 1, N);
        }

        void build(int node, int b, int e) {
            if (b == e) sTree[node] = array[b];
            else {
                int mid = (b + e) >> 1;
                build(node << 1, b, mid);
                build(node << 1 | 1, mid + 1, e);
                sTree[node] = sTree[node << 1] + sTree[node << 1 | 1];
            }
        }

        void pointUpdate(int idx, int val) {
            idx += N - 1;
            sTree[idx] = val;
            while (idx > 1) {
                idx >>= 1;
                sTree[idx] = sTree[idx << 1] + sTree[idx << 1 | 1];
            }
        }

        int query(long s) {
            return query(1, 1, N, s);
        }

        long getCum(int j) {

            return j == 1 ? 0 : query(1, 1, N, 1, j - 1);
        }

        long query(int node, int b, int e, int i, int j) {
            if (b > j || e < i) return 0;
            if (b >= i && e <= j) return sTree[node];
            int mid = (b + e) >> 1;
            long q1 = query(node << 1, b, mid, i, j);
            long q2 = query(node << 1 | 1, mid + 1, e, i, j);
            return q1 + q2;
        }

        //finding the minimum index such that prefixsum[index] >=s
        int query(int node, int b, int e, long s) {
            if (b == e)
                if (sTree[node] >= s) return b;
                else return -1;
            int mid = (b + e) >> 1;
            long left = sTree[node << 1];
            if (left >= s) return query(node << 1, b, mid, s);
            return query(node << 1 | 1, mid + 1, e, s - left);
        }
    }


    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream system) {
            br = new BufferedReader(new InputStreamReader(system));
        }

        public Scanner(String file) throws Exception {
            br = new BufferedReader(new FileReader(file));
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens()) st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        public double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }

        public char nextChar() throws IOException {
            return next().charAt(0);
        }

        public Long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        public boolean ready() throws IOException {
            return br.ready();
        }

        public void waitForInput() throws InterruptedException {
            Thread.sleep(3000);
        }

        public int[] nextIntArray(int n) throws IOException {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        public Integer[] nextIntegerArray(int n) throws IOException {
            Integer[] a = new Integer[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        public double[] nextDoubleArray(int n) throws IOException {
            double[] ans = new double[n];
            for (int i = 0; i < n; i++)
                ans[i] = nextDouble();
            return ans;
        }

    }
}